When the level of confidence and standard deviation remain the same,a confidence interval for a population mean based on a sample of n = 100 will be narrower than a confidence interval for a population mean based on a sample of n = 50.

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Quizplus · Accepted Answer

This is because the standard error, which is the estimate of the standard deviation of the sampling distribution, decreases as sample size increases. A smaller standard error results in a narrower confidence interval. Therefore, a larger sample size leads to a more accurate estimate of the population mean and a narrower confidence interval, assuming that the level of confidence and standard deviation remain the same.

When the Level of Confidence and Standard Deviation Remain the Same,a